Discriminating new physics scenarios at the Next Linear Collider: The role of polarization
E. M. Gregores
Instituto de Fı´sica Teo´rica, Universidade Estadual Paulista, Rua Pamplona 145, 01405–900 Sa˜o Paulo, Brazil
M. C. Gonzalez-Garcia
Instituto de Fı´sica Teo´rica, Universidade Estadual Paulista, Rua Pamplona 145, 01405–900 Sa˜o Paulo, Brazil and Instituto de Fı´sica Corpuscular—IFIC/CSIC, Departament de Fı´sica Teo`rica, Universitat de Vale`ncia,
46100 Burjassot, Vale`ncia, Spain
S. F. Novaes
Instituto de Fı´sica Teo´rica, Universidade Estadual Paulista, Rua Pamplona 145, 01405–900 Sa˜o Paulo, Brazil ~Received 26 March 1997!
We explore the potential of the Next Linear Collider, operating in theegmode, to disentangle new physics scenarios in singleW production. We study the effects related to the exchange of composite fermions in the reactioneg→Wne, and compare them with those arising from trilinear gauge boson anomalous couplings. We stress the role played by the initial state polarization to increase the reach of this machine and to discriminate the possible origin of the new phenomena.@S0556-2821~97!02917-2#
PACS number~s!: 12.60.Rc, 13.88.1e, 14.70.2e
I. INTRODUCTION
The standard model~SM!of the electroweak interactions has received striking confirmation after the recent set of pre-cise measurements made by CERN Large Electron-Positron Collider~LEP! @1#. In particular, the properties of the neutral weak boson and its couplings with fermions were established with great precision. However, similar confidence on other sectors of the SM, such as the vector boson self-couplings which are determined by the non-Abelian gauge structure of the theory, is still lacking. Moreover, the SM does not fur-nish any reasonable explanation for the replication of fermi-onic families and their pattern of mass.
In the search for an explanation for the fermionic genera-tions, we face theories where the known particles ~leptons, quarks, and gauge bosons!are composite@2#, and share com-mon constituents. In this case, the SM should be seen as the low energy limit of a more fundamental theory whose main feature would be the existence of excited states, with mass below or of the order of some large mass scaleL.
Searches for composite states have been carried out by several collaborations of the CERNe1e2 collider LEP@3#,
and also from DESY electron-proton collider HERA@4#. Re-cent data from LEP experiments have excluded excited
spin-1
2electrons with mass up to 80 GeV from the pair production search, and up to 160 GeV from direct single production, for a scale of compositeness f/L.0.7 TeV21 ~see below!. HERA experiments are able to exclude excited electrons with mass below 200 GeV for f/L.4.9 TeV21. Bounds on excited electron couplings have also been established through the evaluation of radiative corrections toZ0width at
one-loop level @5#. On the theoretical side, there have been extensive studies on the possibility of unravelling the exis-tence of excited fermions in p p @6,7#, e1e2 @7–11#, and
e p @9,10#collisions at higher energies.
As pointed out above, another possible source of devia-tion from the SM predicdevia-tions, still allowed by experimental
results, is the existence of anomalous vector boson self-interactions. Our knowledge of the structure of the trilinear couplings between gauge bosons remains rather poor despite several experimental searches have been carried out @12#. One of the main goals of LEPII collider at CERN will be the study of the reaction e1e2→W1W2 which will lead to
stronger bounds on possible anomalous W1W2g and
W1W2Z interactions@13#. There are in the literature several
theoretical studies on the probes for these anomalous inter-actions on future e1e2@14–16#andp p @17#colliders.
An important tool for the search of new physics will be the Next Linear Collider ~NLC!, an e1e2 collider that will
have a center-of-mass energy of at least 500 GeV with an integrated luminosity around 50 fb21 @18#. At the NLC, it will also be possible to obtain a high energy photon beam via the Compton scattering of a laser off the electron beam
@19,20#. The so called laser backscattering mechanism will allow to obtain reactions initiated by eithere1e2,eg, orgg
at NLC.
In this work, we establish the optimum strategy to search for excited fermions in the eg mode of the NLC, which is the most promising one for this purpose. The quest for ex-cited leptons can be carried out in all modes of the collider. In e1e2 collisions, they can be pair produced provided that
their mass is below the kinematical threshold. Above thresh-old the most promising process in e1e2 is via the
t-channel contribution to e1e2→gg. In Ref. @11# it was
shown that better limits are obtained from eg collisions, where the excited lepton can be produced as a resonant state in thes channel@11#.
This search for excited leptons, however, can be jeopar-dized by the misidentification of their signal with other pos-sible sources of new phenomena, such as the anomalous gauge boson self-interactions. Therefore, it is important to study how to isolate the excited fermion signal from the one coming from the anomalous triple vector boson coupling. Recent comparison between the reach of NLC, operating in
56
for the reactions eg→Wne at
A
see5500 GeV due to the exchange of excited spin–12 fermions, and compare them with the deviations arising from anomalous trilinear gauge boson couplings. We make a detailed study of the experi-mental signatures of excited fermions and anomalous cou-plings, exploiting the possibility of polarizing both the elec-tron and laser beams. We design the best strategy to identify the origin of the signal. Our results show that this reaction furnishes stronger limits than the standard reaction eg→eg for excited electrons above the kinematical limit. Further-more, even when the excited electron does not couple to photons, and therefore cannot be produced in the
s-channel, the existence of the corresponding excited neu-trino can be detected in the single W production, via its
t–channel contribution. We also show how the use of polar-ization allows the discrimination between the excited lepton signal and the one due to the anomalous trilinear gauge cou-plings.
The outline of this paper is the following. In Sec. II, we introduce the effective Lagrangians describing the excited fermion and anomalous gauge bosons couplings, and in Sec. III we present the main ingredients of the laser backscatter-ing mechanism with polarized beams. Section IV contains the analysis of the reaction eg→Wne and displays our
re-sults. Finally, in Sec. V, we summarize our conclusions.
II. EFFECTIVE LAGRANGIANS
In order to describe the effects of new physics due to both the presence of new excited leptons and to anomalous trilin-ear couplings we make use of the effective Lagrangian ap-proach. For the excited states, we concentrate in a specific model @9#, which has been extensively used by several ex-perimental collaborations@3,4#. In doing so, we introduce the weak doublets, for the usual left-handed fermion (cL) and for the excited fermions (C*), and we write the most gen-eral dimension-five effective Lagrangian describing the cou-pling of the excited fermions to the usual fermions, which is SU~2!3U~1!invariant andC P conserving,
LF f521 2L C¯*s
mn
S
g fti
2Wmn
i
1g
8
f8
Y2Bmn
D
cL1H.c.,~1!
where f and f
8
are weight factors associated to the SU~2!and U~1! coupling constants ~g and g
8
!, with L being the compositeness scale, and smn5(i/2)@gm,gn#. We assume a pure left-handed structure for these couplings in order toCZEe52 e
4L~f cotuW2f
8
tanuW!,CgNn5
e
4L~f2f
8
!, CZNn5e
4L~f cotuW1f
8
tanuW!,CWEn5CWNe5 e
2& sinuWL
f, ~3!
whereuWis the weak angle with tanuW5g
8
/g.For the trilinear gauge coupling, we also write the most generalC- andP-conserving interaction Lagrangian between the charged gauge bosons and the photon which is U~1!em
invariant @22#:
L52ie
F
g1g~Wmn† WmAn2Wm†WmnAn!1kgWm†WnFmn1 lg
MW2 Wtm
†
WnmFnt
G
. ~4!For on-shell photons, g1g51 is fixed by electromagnetic gauge invariance since it determines the W electric charge. The coefficientsk~l!assumes the values 1~0!in the SM, and are related to the magnetic moment, mW, and the electric quadrupole moment, QW, of theW boson, according to
mW5 e
2MW~11kg1lg! and QW52 e
MW2 ~kg2lg!.
In this paper, we are interested in analyzing the influence of both excited fermion and anomalous vector boson cou-pling in the reaction eg→Wne. The contributions of these new particles and interactions are represented in Fig. 1 as double lines and black dot, respectively.
III. POLARIZED LASER BACKSCATTERING
The electron beam of a linear collider can be transformed into a intense photon beam via the process of laser back-scattering@19#. The basis of this mechanism lays on the fact that Compton scattering of energetic electrons by soft laser photons results into high energy photons, collimated in the direction of the incident electron.
F~x,z;Pe,Pl!5 2pa 2
zm2sc
F
1
12x112x24r~12r!
2PePlrz~2r21!~22x!
G
, ~5!wherePeis the mean electron longitudinal polarization,Plis
the laser photon circular polarization, andscis the Compton
cross section, which can be written as
sc5sc
0
1PePlsc
1
, ~6!
with
sc052pa 2
zm2
FS
124 z2
8
z2
D
ln~z11!11 21
8 z2
1 2~z11!2
G
,sc1 52pa
2
zm2
FS
112
z
D
ln~z11!2 5 211 z112
1 2~z11!2
G
.~7!
We have defined the variables
x5v
E, z5
4Ev0
m2 , r5 x
z~12x!, ~8!
wherem andE are the electron mass and energy, v0 is the
laser energy and v is the backscattered photon energy. The variablex<xmax[z/(z11) represents the fraction of the
elec-tron energy carried by the back scattered photon. A cutoff value z52(11&).4.83 is assumed in order to avoid the threshold for electron-positron pair creation through the in-teraction of the laser and the backscattered photons. The backscattered photon spectrum~5!depends only on the prod-uct PePl, and as can be seen from Fig. 2~a!, for negative
values of this product the spectrum is dominated by hard photons.
A very powerful feature of the Compton backscattering mechanism is the possibility of obtaining a high degree of polarization for the backscattered photons by polarizing the incoming electron and the laser beams. The mean backscat-tered photon helicity is given by the Stokes parameter
j251
D
H
Perz@11~12x!~2r21!2#
2Pl~2r21!
F
1
12x112x
GJ
, ~9!where
D511
2x112x24r~12r!2PePlrz~2r21!~22x!.
~10!
Forx5x max~orr51! andPe50 or Pl561, we have j252Pl, i.e., the polarization of the backscattered photon
beam has the opposite value of the laser polarization. One can also see that for x5z/(z12) ~or r51/2! the Stokes parameter j2 is independent of the laser polarization @see
Fig. 2~b!#, and is given by
j2~r51/2!
5Pe
z~z12!
z~z12!14. ~11!
The cross section for the reaction ge→X in an electron-positron linear collider where the electron-positron beam, with longi-tudinal polarization Pp, is converted into a backscattered
photon beam, is given by
dsPej2~ge→X!5k
E
xminxmax
dxF~x,z;Pp,Pl!dsˆPej2~eg→X!,
~12!
wherekis the efficiency of the laser conversion of the elec-trons into photons and dsˆP
ej2 is the polarized cross section for the subprocess ge→X, which is a function ofsˆ5xs. In our calculation we assume that 100% of the electrons are converted into photons (k51).
The polarized subprocess cross section can be written as FIG. 1. Feynman diagrams contributing to the process
eg→Wne in presence of excited fermions ~double lines! and anomalous vector boson coupling~black dot!.
dsˆP
ej25 1
4@~11Pej2!~dsˆ111dsˆ22!
1~Pe1j2!~dsˆ112dsˆ22!1~12Pej2!~dsˆ12
1dsˆ21!1~Pe2j2!~dsˆ122dsˆ21!#, ~13!
with dsˆl
elg (le(g)561) being the polarized subprocess cross section for full electron and photon polarization, Pe is
the longitudinal polarization of the electron beam, and the Stokes parameter, j2, is given in Eq.~9!.
IV. RESULTS
A. Excited fermions signature
The standard mechanism to establish the existence of an excited electron with mass below the kinematical reach of theeg machine is the identification of the Breit-Wigner pro-file in the eg invariant mass distribution of the process
eg→eg @11#. This is obviously only possible when the ex-cited electron couples to the photon, i.e., fÞ2f
8
@see Eq.~3!#. On the other hand, the reactioneg→Wneis sensitive to
both the exchange of the excited electron in the s channel and to the exchange of the excited neutrino in the t channel
~see Fig. 1!. The characteristic signature of the excited lep-tons will therefore depend on the excited fermion mass and on the relative weight of thes-channel versus the t-channel contribution or, in other words, the relative sizes of f and
f
8
.As in the reaction eg→eg, the existence of an excited electron with nonvanishing coupling to the photon and with mass below the kinematical reach of theegcollider, can also be easily identified in the reaction eg→Wne but now through the study of the W transverse momentum distribu-tion, ds/d pT. For illustration, we present in Fig. 3 the pT
distribution of theWproduced in the reactioneg→Wne, for
ME5350 GeV at ane1e2collider with
A
s5500 GeV. We introduced a cut of 15° in the polar angle ~u! of the detect-able final state particles with the beam pipe to ensure their detection. We also assumed a reconstruction efficiency of 60% for the produced W’s. As expected, the existence of excited states with mass below the kinematical reach of the
eg collider provides an very clear signal, the Jacobian peak at pT;ME/2. This situation will be no longer considered
here, since our main concern is the possibility of misidenti-fication of new physics effects on the NLC, and in this sce-nario, the existence of excited fermions can easily be set apart from the anomalous vector boson contribution.
For excited leptons above the kinematical limit of the col-lider we still find an enhancement on the total cross section due to the s-channel contribution. We also find an effect in the distribution of the producedW. We have simulated these distributions for ME5L5500 GeV and f5f
8
. We present on Fig. 4 the transverse momentum distribution, and the angle between the W and the electron beam direction for unpolarized beams. As seen in the figure, the existence of excited fermions leads to an enhancement ofWproduction at large pT which reflects the tail of the jacobian peak. In theangular distribution of the W the effect of composition is very small.
The process mediated by the exchange in thet-channel of excited neutrinos coupled to photons takes place when f
Þf
8
, and gives a much smaller effect. This process is par-ticularly interesting in the extreme situation when f52f8
since, in this case, CgEe vanishes, and just the t-channel
diagram contributes. This contribution gives rise to a de-structive interference which diminishes the total W yield, without altering the shape of the transverse momentum and angular distributions in a significant way ~see Fig. 5!.
In order to estimate the reach of an eg collider to search for new physics, we defined the statistical significance of the signal~S!as
FIG. 3. Tranverse momentum distribution of W bosons in the presence of an excited electron with ME5350 GeV, compared to the SM prediction, for f5f851, andL51 TeV.
S[usnew2sSMu
A
sSMA
Lee, ~14!wheresnew (sSM) is the total cross section for new physics ~standard model!contributions, andLeeis the integrated lu-minosity of the machine. We will assume Lee550 pb21 for
the NLC. In order to ensure that the event is well within the detector volume, we restrict the polar angle of all detectable final particles with the beam pipe to be smaller than 15° (ucosuu<0.97). With this requirement, we assumed that 60% of the produced W’s can be properly reconstructed.
In Fig. 6, we show the discovery limits for the composite state in theL3ME plane for botheg andWne final states,
requiring a 3seffect in the total cross section. For
unpolar-ized photons theeW channel leads to stronger limits than the
eg channel which has large background coming from Comp-ton scattering. However an excess in the eg production is a definite signal of compositeness, since there is no contribu-tion of anomalous couplings in this channel. Moreover, as mentioned above, if the weight factorsf andf
8
are such thatf52f
8
, the signal of composition on theeg production will disappear completely, but survive on single W production through the exchange of a neutral composite fermion on thet channel. The discovery limit of the NLC for such neutral states is shown in Fig. 7.
Polarization can be used to improve the discovery region in theL3M plane through the enhancement of the luminos-ity and the cross section. The photon distribution functions assume approximately the same value at ¯x5z/(z12)
.0.71, even for different polarization configurations of the initial particles ~see Fig. 2!. In the interval 0,x,¯x, the luminosity is higher for PpPl.0, whereas for the range x.¯xthe distribution withPpPl,0 dominates. Therefore, in order to search for excited electrons with mass above
ME5
A
¯sx , we should employ the polarization configurationsof the positron and the laser in such a way thatPpPl,0. The
degree of circular polarization of the scattered photon, j2,
has the same sign as the positron polarization in the region of interest. Because of the chiral nature of the weak interac-tions, just left-hand electrons will produce W’s, and there-fore, only electrons and photons with negative helicity con-tribute to the exchange of an excited electron in the s
channel. In this case, the best strategy is to require that the electron and positron have negative polarization, while the laser is set up with positive polarization. We assume that 90% of beam polarization is achievable at the NLC and that the laser can be 100% polarized~i.e.,Pe25Pe1520.9, and
Pl51). With this setup the discovery region can be enlarged
as much as shown on Fig. 6.
The situation changes when we are dealing with the pro-cess involving the excited neutrino. As before, just left-FIG. 5. The same as Fig. 4, for f5f8521, and
MN5L5300 GeV.
FIG. 6. Discovery contour for f5f851. Inside the shaded re-gions the deviations from SM are greater 3s. We excluded the unphysical region whereL,ME.
handed electrons will participate in the reaction and again one must choosePe2,0, but now the photon line is attached
to the final state neutrino, and consequently, just the positive helicity photons couple to the fermionic line. According to the discussion above, to obtain a highly energetic and posi-tively polarized photon beam, we must set the positron po-larization to be positive (Pe150.9) and the laser
polariza-tion to be negative (Pl521). However, one must also
notice that in this process, when the positron and laser have positive polarization, most of the photons have positive he-licity~except the very high energy ones!while, at the same time, the SM background coming from the diagram with self-boson interaction is reduced. Due to this reduction, the configuration Pe252Pe1520.9 andPl51 leads to better
limits as can be seen in Fig. 7.
B. Anomalous gauge boson couplings: Comparison
Let us now examine the consequences of the existence of trilinear anomalous couplings in the singleW production. In order to clarify the effect of each of the two possible anoma-lous couplings~Dkgandlg!, we envisaged two distinct sce-narios, by keeping just one of them different from zero at a time. In Fig. 8, we show the angular and transverse momen-tum distributions for different values ofDkg512kg while keeping lg50. We can see from these figures that the only effect of varying Dkg is to increase or decrease the total cross section depending on its sign, while producing small effect on the shape of the distributions. The number of ob-served events is larger~smaller!than the SM expectation for
Dkg.0 (Dkg,0).
Conversely, in Fig. 9, we show the angular and transverse momentum distributions for different values of lg while keeping Dkg50. We can see in these figures that the cross section is always larger than the SM prediction for any sign of the couplinglg. The presence of a nonvanishinglgalso increases the number of W’s produced in the central and forward direction and of those produced with high pT.
Polarization has also proven to be very useful to unravel the existence of anomalous couplings, and the discovery lim-its for anomalous couplings have been extensively covered elsewhere @15#. In what follows we will concentrate on the possibility of distinguishing these effects from those arising from the existence of the excited leptons.
Let us now discuss the different scenarios we can face when the NLC starts its operation. It will probably start on its unpolarized mode, in order to be as ‘‘democratic’’ as possible to discover new physics. The first observable that the accumulated statistics will allow to measure is the total cross section. From what we saw above, the effect of new physics can either increase or decrease the total W produc-tion.
If the number of produced W’s is greater than expected, one should just look into theegevents that will be produced at the same time. As we saw, in the framework where com-position leads to an enhancement on the total singleW cross section, theeg channel is also very sensitive to the presence of excited leptons. An increase in theeg cross section would indicate that the excess of W is due to the existence of an excited electron. If no excess is seen in theeg channel, like-lihood fittings to the angular and transverse momentum dis-tributions will be able to determine the anomalous coupling parameters leading to such deviations.
On the other hand, if the total cross section is smaller than predicted by the SM, two possibilities remain:~i!the trilinear coupling is anomalous with the value ofDkg<0, or,~ii!the excited neutrino exists, and its gauge structure is such that
f.2f
8
. To tell these two possibilities apart, we define the polarization asymmetryApol5DDss122Ds21
121Ds21, ~15!
where, for instance,
Ds125s12SM2s12obs ~16!
FIG. 8. Effects of a variation onDkg inW kinematical distri-butions, compared with the standard model (Dkg50).
measures the deviation from the SM prediction when the positron and laser polarizations are set Pe150.9 and
Pl521, always keeping Pe2520.9. Correspondingly,
Ds21 measures the deviation from the SM prediction for
Pe1520.9 and Pl51.
In Fig. 10, we plot Apolfor the two type of models here
considered. As seen in this figure, the asymmetry due to the presence of anomalous trilinear gauge couplings lg50 and
Dkg<0 is always negative and very small. On the contrary, the presence of excited neutrinos would yield a larger posi-tive asymmetry. This occurs because photons with both po-larizations contribute to the anomalousDkgterm, while only positive helicity photons enter in the excited neutrino contri-bution. Therefore in both configurations the reduction in the cross section due to the negative Dkg is of the same order and the corresponding asymmetry is small. However in the configuration ~12!, since most of the high energy photons have positive helicity, the effect of the excited neutrino con-tribution is enhanced and the destructive interference is larger. ConsequentlyDs12@Ds21, what gives a positive and larger asymmetry.
V. CONCLUSION
In this work, we have studied the deviations from the SM predictions for the reactions eg→Wne at
A
see5500 GeVdue to two possible sources of new physics. We have ana-lyzed the effect associated to the existence of excited spin–
1
2 fermions, and we have compared them to those arising from anomalous trilinear couplings between the gauge bosons. We have discussed how the use of polarization can improve the reach of the machine in the search for excited fermions. Our results show that this reaction can furnish stronger limits than the standard reactioneg→egfor excited electrons above the kinematical limit. We have shown how, by setting up the electron, positron, and laser polarizations, we can be sensitive to scales,L, up to 9 TeV, which is twice the bound obtained just with unpolarized beams. Our results show that excited electrons coupling to photons with strength
e can be ruled out forME<1 TeV. In addition, the
simulta-neous analysis of both eg andWne channels allows to
dis-criminate the excited electron signature from the one due to the presence of anomalous trilinear gauge couplings which would lead to the same increase in the total W yield.
Single W production is also the main channel to look for excited neutrinos when the corresponding excited electron does not couple to photons. In this case, we get a reduction in the number of events, as compared to the SM prediction, due to the destructive interference between the SM contribu-tion and the one due to the exchange of the excited neutrino in thetchannel. This reduction is significative enough to rule out excited neutrinos withMN<1 TeV. Anomalous trilinear couplings with very smalllgandDkg<0 would also lead to a decrease in the number of events which could fake the existence of an excited neutrino. For this case we have intro-duced a polarization asymmetry which is sensitive to the origin of the deviation.
ACKNOWLEDGMENTS
M.C. Gonzalez-Garcia is grateful to the Instituto de Fı´sica Teo´rica of the Universidade Estadual Paulista for its kind hospitality. This work was supported by Fundac¸a˜o de Am-paro a` Pesquisa do Estado de Sa˜o Paulo, by DGICYT under Grant No. PB95-1077, by CICYT under Grant No. AEN96-1718, and by Conselho Nacional de Desenvolvimento Cien-tı´fico e Tecnolo´gico.
@1#The LEP Collaborations ALEPH, DELPHI, L3, OPAL, and the LEP Electroweak Working Group, contributions to the 28th International Conference on High-Energy Physics ~ICHEP 96!, Warsaw, Poland, 1996@Report No. CERN-PPE/ 96-183, 1996~unpublished!#.
@2#For a review, see, for instance, H. Harari, Phys. Rep.104, 159 ~1984!; M. E. Peskin, inProceedings of the International Sym-posium on Lepton and Photon Interactions at High Energies, Kyoto, Japan, 1985, edited by M. Konuma and K. Takahashi ~RIFP, Kyoto, 1986!, p. 714; H. Terazawa, inProceedings of
the XXII International Conference on High Energy Physics, Leipzig, Germany, 1984, edited by A. Meyer and E. Wiec-zorek~Akademic derwissenschaften der OCR Zeipten, 1984!, p. 63; W. Buchmu¨ller, Acta Phys. Austriaca Suppl. 27, 517 ~1985!.
@3#ALEPH Collaboration, D. Buskulinet al., Phys. Lett. B385, 445 ~1996!; OPAL Collaboration, K. Ackerstaff et al., ibid. 391, 197~1997!; DELPHI Collaboration, P. Abreuet al.,ibid. 393, 245~1997!; L3 Collaboration, M. Acciarriet al., Report No. CERN-PPE-97-012, 1997~unpublished!.
Otwinowska, Z. Phys. C55, 163~1992!; J. C. Montero and V. Pleitez, Phys. Lett. B321, 267~1994!.
@9#K. Hagiwara, S. Komamiya, and D. Zeppenfeld, Z. Phys. C29, 115~1985!.
@10#F. Boudjema, A. Djouadi, and J. L. Kneur, Z. Phys. C57, 425 ~1993!.
@11#I. F. Ginzburg and D. Yu. Ivanov, Phys. Lett. B 276, 214 ~1992!; T. Kon, I. Ito, and Y. Chikashige, ibid. 287, 277 ~1992!; E. Boos, A. Pukhov, and A. Beliaev, ibid. 296, 452 ~1992!; O. J. P. E´boli, E. M. Gregores, J. C. Montero, S. F. Novaes, and D. Spehler, Phys. Rev. D53, 1253~1996!. @12#CLEO Collaboration, M. S. Alamet al., Phys. Rev. Lett.74,
2885~1995!; CDF Collaboration, F. Abeet al.,ibid.74, 1936 ~1995!; D0 Collaboration, S. Abachi et al., ibid. 75, 1023 ~1995!.
@13#G. Gounariset al., inPhysics at LEP2, edited by G. Altarelli, T. Sjo¨strand, and F. Zwirner~CERN, Geneva, 1996!, Vol. 1, p. 525, hep-ph/9601233.
@14#e1e2Collisions at 500 GeV: The Physics Potential
~Proceed-Planning Study,’’ to be published in Electroweak Symmetry Breaking and Beyond the Standard Model, edited by T. Bark-low, S. Dawson, H. Haber, and J. Seigrist ~Report No. hep-ph/9503425!.
@18#See, for instance, the Next Linear Collider R&D Homepage,
http://nlc.physics.upenn.edu/nlc/nlc.html, and the NLC Zeroth-Order Design Report at http:// www.slac.stanford.edu/accel/nlc/zdr/
@19#F. R. Arutyunian and V. A. Tumanian, Phys. Lett. 4, 176 ~1963!; R. H. Milburn, Phys. Rev. Lett. 10, 75~1963!; I. F. Ginzburg, G. L. Kotkin, V. G. Serbo, and V. I. Telnov, Nucl. Instrum. Methods Phys. Res. 205, 47 ~1983!; V. I. Telnov, Nucl. Instrum. Methods Phys. Res. A294, 72~1990!. @20#I. F. Ginzburg, G. L. Kotkin, V. G. Serbo, and V. I. Telnov,
Nucl. Instrum. Methods Phys. Res. A219, 5~1984!.
@21#S. J. Brodsky and S. D. Drell, Phys. Rev. D22, 2236~1980!; F. M. Renard, Phys. Lett.116B, 264~1982!.
